Question

Ans this question fast plzz 6 *

Answer 1

$\huge{\mathfrak{Heyaa\:Mate}}$

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$\huge\sf{Answer}$

${\red{\boxed{{y}^{2} - 2y - 7 = 0}}}$

$1) \: { \alpha }^{2} + { \beta }^{2} \\ = > \alpha + \beta = \frac{ - b}{a} \\ = > a = 1 \\ = > b = - 2 \\ = > c = - 7 \\ = > \alpha + \beta = \frac{ - ( - 2)}{1} \\ = > \alpha + \beta = 2 \\ = > \alpha \beta = \frac{c}{a} \\ = > \alpha \beta = \frac{ - 7}{1} \\ = > \alpha \beta = - 7$

${\red {\boxed{{( \alpha + \beta) }^{2} = { \alpha }^{2} + { \beta }^{2} + 2 \alpha \beta}}}$

$putting \: the \: value \: of \: ( \alpha \beta ) \: \\ ( \alpha + \beta ) \: in \: the \: above \: formulae$

$= > {2}^{2} = { \alpha }^{2} + { \beta }^{2} + 2( - 7) \\ = > 4 = { \alpha }^{2} + { \beta }^{2} - 14 \\ = > 4 + 14 = { \alpha }^{2} + { \beta }^{2}$

${\green{\boxed{ { \alpha }^{2} + { \beta }^{2} = 18}}}$

$2) { \alpha }^{3} + { \beta }^{3}$

${\red{\boxed{ {( \alpha + \beta) }^{3} = { \alpha }^{3} + { \beta }^{3} + 3 \alpha \beta (\alpha + \beta)}}}$

$putting \: the \: value \: of \: ( \alpha \beta ) \: \\ ( \alpha + \beta )in \: above \: formulae$

$= > {2}^{3} = { \alpha }^{3} + { \beta }^{3} + 3( - 7)(2) \\ = > 8 = { \alpha }^{3} + { \beta }^{3} - 42 \\ = > 8 + 42 = { \alpha }^{3} + { \beta }^{3}$

${\green {\boxed{50 = { \alpha }^{3} + { \beta }^{ 3}}}}$

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$\huge{\mathfrak{Thanks}}$

Answer 2

here is your answer i hope it helps you